From left, Will Gow, Henry Adams and Henry Worsley on Christmas Day on their centenary expedition to the south pole

At new year 2009, three men reached the south pole in what was an unusual expedition. What marked out this feat wasn't just that none of them was a regulation explorers – one was a lawyer, another a City worker, the third a soldier – but that the main criterion for joining the team was that they all had to be related to members of an expedition that had tried – and failed – to reach the pole a century before.

Of this team selected by genes rather than experience, Henry Adams was a late addition, and one who probably best exemplifies how the pull of an illustrious ancestor can exert its way down the generations.

Every family has its legendary figures, but not many have an ancestor so pivotal in the history of polar exploration that a mountain has been named after him. Jameson Boyd Adams is one of these: second-in-command to the Antarctic pioneer Ernest Shackleton for his 1908-09 Nimrod expedition to the south pole, and a larger-than-life character, his heroic exploits have been treasured by the Adams family ever since.

So large, in fact, that when his great-grandson, Henry, was offered the chance to follow in his hallowed footsteps 100 years later, there was really only one answer for the man who had been steeped in stories about this illustrious ancestor since he was a boy.

"You just have to look at a map," urges Henry, 36, from Suffolk. "Antarctica is the highest, wildest, most desolate place on earth. To think of those men setting out to conquer it, armed with nothing but tweeds and derring-do … it's enough to grip any child."

Shackleton is perhaps most famous for his subsequent Endurance expedition, between 1914 and 1917, which set out to cross the Antarctic. Although it failed, it cemented him in the annals of polar exploration after he successfully led his team to safety.

But it was his earlier attempt to reach the south pole that first catapulted him to popular attention. On 9 January 1909, Shackleton, with Adams, Frank Wild and Eric Marshall, reached a new furthest south point, 97 miles short of the pole. But a shortage of supplies forced them into turning back and racing against starvation to base.

Despite failing to attain its goal, the expedition was feted on its return to England, and Shackleton received a knighthood. His wife, Emily, remembered: "The only comment he made to me about not reaching the pole was: 'A live donkey is better than a dead lion, isn't it?' and I said, 'Yes, darling, as far as I am concerned.'"

This was the adventure that cemented Jameson's place in Adams family lore, and which resonated down the generations to Henry.

But Henry nearly didn't make it on to the 2009 expedition. "I was busy as a lawyer, about to start a family, and my sister heard some bloke called Will Gow talking about a plan to stage an expedition to celebrate the centenary, using descendants." At first, Henry was on the reserve team but after various would-be explorers changed their minds, team leader Henry Worsley – whose account of the expedition is thrillingly detailed in his book In Shackleton's Footsteps – offered Henry third place, alongside himself and Gow.

Worsley described the process of building the team as "gene-pool selection", something Henry was happy to go along with – Jameson had cast a concentrated spell of fascination over his whole life. "I was aware of him from my earliest years – he was an absolute beacon for the whole family. He was my father's father's father. My grandfather lived slightly in the shadow of Jameson, who was an enormous personality and gave a lot to the world. He was known mainly as 'The Mate'. He called everyone 'mate' – he even called the King 'mate'. I was the kind of child who spent the first eight years of his life up a tree. Jameson had played in my mind since then – for Antarctica, and for being such a remarkable character.

"I wish I knew more about what he went through personally. I can only imagine how it must have felt to get within 97 miles of the pole, the closest in history at the time, having sacrificed and risked so much over many months, before having to turn back in order to stay alive as their supplies dwindled."

Jameson – later Sir Jameson – was a colourful, determined individual who ran away from home as a youth to join the merchant navy, swore freely, and exerted a warm, powerful charisma. After returning from the Nimrod expedition, he joined the civil service, but was recalled to the navy at the start of the first world war. He was awarded the Distinguished Service Order and the Croix de Guerre, but was invalided out after a head wound. He rejoined the civil service, then became secretary of King George's Jubilee Trust For Youth; in the second world war he rejoined the services and was, again, distinguished. In 1948, he was knighted.

"He took absolutely everyone at face value, and everyone seemed to know him." Henry's father told tales of being taken to Jameson's club, White's. "He lived there for many years, paid for by the other members because he was such good value," recounts Henry. "The waiter would say 'Sir Jameson, what can we recommend?' And he'd reply: 'Did the waiter piss in the soup?' And the waiter would say: 'Oh no, sir.' He'd say: 'I won't have it then.'"

But tales of Ripping-Yarns-style naughtiness are not the only reason that the young Henry grew up idolising the great-grandfather who died in 1962, 15 years before he was born. "He was so much his own man – a real maverick," says Henry. "He devoted his later years to youth development and that's one of the reasons he hobnobbed in high society; he'd tap up the king, whom he knew, for funds."

Following on from a man with such a reputation must have been daunting, but Henry went one better than Jameson, because instead of turning back, he, Worsley and Gow completed the final 97-mile leg to the south pole – and en route they saw Adams Mountain.

This was an astonishing moment for Henry. He and his teammates had spent eight days battling the terrifying Beardmore Glacier, hauling their sledges over the treacherous ice field with broken crampons strapped so tightly that they caused lasting damage to their feet. "And then, you've got your great-grandfather's mountain standing to your right," he says. "I felt the most intense feeling of joy and privilege. I looked at the mountain, and it was a lovely feeling of kinship. I thought: you really earned the right to have a mountain named after you."

Each night, the team would read that day's extract from Shackleton's diary. It's a matter of great sadness to Henry that Jameson's diary was lost. "It was burnt in the Harrods depositary fire during the war," he says. "I think The Mate's diaries would have been so colourful."

Henry learned through the expedition that he has something else of Jameson in his makeup. "He didn't like self-aggrandisement and plaudits, and one thing I learned about myself is that you derive satisfaction from what you have done, not what other people think of it. You get laid bare on an expedition like that and you know whether you like yourself or not. You know whether you shaped up, or not, as a person. The Mate had that innately, and I learned it on the expedition." Does Henry think he has other similarities to his illustrious ancestor?

"Jameson was a great spinner of yarns, and this is a great thing to spin a yarn about. He was a jovial sort, and I am a jovial sort," concedes Henry. "The optimism is important. If you put your head around what you're actually doing, it's a monumentally boring task. You are three guys pulling weight – that's all you are – so keeping your spirits up is important. I value few things more than banter and I love a good laugh."

Henry says the support of his wife, Alex, and that of his parents made it possible for him to go. "Alex is selfless – not just to allow me to do it, but to want me to do it, which makes all the difference. And my mother and father too. Being happy – being positive – is the only thing you need in the Antarctic."

He would "go back tomorrow" to the Antarctic and felt devastated to leave. "It's so vast, you lay yourself open, really, as there's nothing else to do. You're pitting yourself against something so hostile it wants you dead – but it wants you to live very vividly in doing so."

Shackleton is a hero to many polar explorers but to Henry, Jameson's brand of heroism is even more impressive. "If there is one person I would have liked to have met, it's him. Shackleton is overtly heroic, and what he achieved was mind-boggling – that he defied the odds and came back with his men intact is awesome. But he's not a hero of mine – he's a man who did heroic things. Jameson, however, didn't seek accolades – he would just go about his business in a unique fashion and with an unassailable integrity. He was the strongest of men, and the closest thing I have to a hero – and he happens to be my great-grandfather."

In Shackleton's Footsteps: A Return to the Heart of the Antarctic by Henry Worsley (Virgin Books, £18.99). To order a copy for £15.19 with free UK p&p, go to theguardian.com/bookshop or call 0330 333 6846